"""
Lhs functions are inspired by
https://github.com/clicumu/pyDOE2/blob/
master/pyDOE2/doe_lhs.py
"""
import numpy as np
from sklearn.utils import check_random_state
from scipy import spatial
from ..space import Space, Categorical
from .base import InitialPointGenerator
def _random_permute_matrix(h, random_state=None):
rng = check_random_state(random_state)
h_rand_perm = np.zeros_like(h)
samples, n = h.shape
for j in range(n):
order = rng.permutation(range(samples))
h_rand_perm[:, j] = h[order, j]
return h_rand_perm
[docs]class Lhs(InitialPointGenerator):
"""Latin hypercube sampling
Parameters
----------
lhs_type : str, default='classic'
- 'classic' - a small random number is added
- 'centered' - points are set uniformly in each interval
criterion : str or None, default='maximin'
When set to None, the LHS is not optimized
- 'correlation' : optimized LHS by minimizing the correlation
- 'maximin' : optimized LHS by maximizing the minimal pdist
- 'ratio' : optimized LHS by minimizing the ratio
`max(pdist) / min(pdist)`
iterations : int
Defines the number of iterations for optimizing LHS
"""
[docs] def __init__(self, lhs_type="classic", criterion="maximin",
iterations=1000):
self.lhs_type = lhs_type
self.criterion = criterion
self.iterations = iterations
[docs] def generate(self, dimensions, n_samples, random_state=None):
"""Creates latin hypercube samples.
Parameters
----------
dimensions : list, shape (n_dims,)
List of search space dimensions.
Each search dimension can be defined either as
- a `(lower_bound, upper_bound)` tuple (for `Real` or `Integer`
dimensions),
- a `(lower_bound, upper_bound, "prior")` tuple (for `Real`
dimensions),
- as a list of categories (for `Categorical` dimensions), or
- an instance of a `Dimension` object (`Real`, `Integer` or
`Categorical`).
n_samples : int
The order of the LHS sequence. Defines the number of samples.
random_state : int, RandomState instance, or None (default)
Set random state to something other than None for reproducible
results.
Returns
-------
np.array, shape=(n_dim, n_samples)
LHS set
"""
rng = check_random_state(random_state)
space = Space(dimensions)
transformer = space.get_transformer()
n_dim = space.n_dims
space.set_transformer("normalize")
if self.criterion is None or n_samples == 1:
h = self._lhs_normalized(n_dim, n_samples, rng)
h = space.inverse_transform(h)
space.set_transformer(transformer)
return h
else:
h_opt = self._lhs_normalized(n_dim, n_samples, rng)
h_opt = space.inverse_transform(h_opt)
if self.criterion == "correlation":
mincorr = np.inf
for i in range(self.iterations):
# Generate a random LHS
h = self._lhs_normalized(n_dim, n_samples, rng)
r = np.corrcoef(np.array(h).T)
if len(np.abs(r[r != 1])) > 0 and \
np.max(np.abs(r[r != 1])) < mincorr:
mincorr = np.max(np.abs(r - np.eye(r.shape[0])))
h_opt = h.copy()
h_opt = space.inverse_transform(h_opt)
elif self.criterion == "maximin":
maxdist = 0
# Maximize the minimum distance between points
for i in range(self.iterations):
h = self._lhs_normalized(n_dim, n_samples, rng)
d = spatial.distance.pdist(np.array(h), 'euclidean')
if maxdist < np.min(d):
maxdist = np.min(d)
h_opt = h.copy()
h_opt = space.inverse_transform(h_opt)
elif self.criterion == "ratio":
minratio = np.inf
# Maximize the minimum distance between points
for i in range(self.iterations):
h = self._lhs_normalized(n_dim, n_samples, rng)
p = spatial.distance.pdist(np.array(h), 'euclidean')
if np.min(p) == 0:
ratio = np.max(p) / 1e-8
else:
ratio = np.max(p) / np.min(p)
if minratio > ratio:
minratio = ratio
h_opt = h.copy()
h_opt = space.inverse_transform(h_opt)
else:
raise ValueError("Wrong criterion."
"Got {}".format(self.criterion))
space.set_transformer(transformer)
return h_opt
def _lhs_normalized(self, n_dim, n_samples, random_state):
rng = check_random_state(random_state)
x = np.linspace(0, 1, n_samples + 1)
u = rng.rand(n_samples, n_dim)
h = np.zeros_like(u)
if self.lhs_type == "centered":
for j in range(n_dim):
h[:, j] = np.diff(x) / 2.0 + x[:n_samples]
elif self.lhs_type == "classic":
for j in range(n_dim):
h[:, j] = u[:, j] * np.diff(x) + x[:n_samples]
else:
raise ValueError("Wrong lhs_type. Got ".format(self.lhs_type))
return _random_permute_matrix(h, random_state=rng)
